#install.packages("forecast")
#install.packages("plotly")
#install.packages("tidyr")
#install.packages("dplyr")
library(forecast)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
data(EuStockMarkets)
summary(EuStockMarkets)
## DAX SMI CAC FTSE
## Min. :1402 Min. :1587 Min. :1611 Min. :2281
## 1st Qu.:1744 1st Qu.:2166 1st Qu.:1875 1st Qu.:2843
## Median :2141 Median :2796 Median :1992 Median :3247
## Mean :2531 Mean :3376 Mean :2228 Mean :3566
## 3rd Qu.:2722 3rd Qu.:3812 3rd Qu.:2274 3rd Qu.:3994
## Max. :6186 Max. :8412 Max. :4388 Max. :6179
class(EuStockMarkets)
## [1] "mts" "ts" "matrix"
par(mfrow=c(4,1))
x <- seq_len(nrow(EuStockMarkets))
for (i in seq_len(ncol(EuStockMarkets))) {
y <- EuStockMarkets[,i]
heading <- colnames(EuStockMarkets)[i]
plot(x, y, type="n", main = heading, xaxt = "n")
lines(x, EuStockMarkets[,i])
years <- as.integer(time(EuStockMarkets))
tick.posis <- seq(10, length(years), by = 100)
axis(1, at = tick.posis, las = 2, labels = years[tick.posis])
}
plot(EuStockMarkets)
library(plotly)
## Loading required package: ggplot2
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(tidyr)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
stocks <- as.data.frame(EuStockMarkets) %>%
gather(index, price) %>%
mutate(time = rep(time(EuStockMarkets), 4))
plot_ly(stocks, x = ~time, y = ~price, color = ~index, mode = "lines")
## No trace type specified:
## Based on info supplied, a 'scatter' trace seems appropriate.
## Read more about this trace type -> https://plotly.com/r/reference/#scatter
ftse=(EuStockMarkets[,4])
plot(ftse)
components.ts = decompose(ftse)
plot(components.ts)
fit_ftse <- auto.arima(ftse, trace=TRUE)
##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,1,2)(1,0,1)[260] with drift : Inf
## ARIMA(0,1,0) with drift : 17994.59
## ARIMA(1,1,0)(1,0,0)[260] with drift : Inf
## ARIMA(0,1,1)(0,0,1)[260] with drift : Inf
## ARIMA(0,1,0) : 17997.78
## ARIMA(0,1,0)(1,0,0)[260] with drift : Inf
## ARIMA(0,1,0)(0,0,1)[260] with drift : Inf
## ARIMA(0,1,0)(1,0,1)[260] with drift : Inf
## ARIMA(1,1,0) with drift : 17968.54
## ARIMA(1,1,0)(0,0,1)[260] with drift : Inf
## ARIMA(1,1,0)(1,0,1)[260] with drift : Inf
## ARIMA(2,1,0) with drift : 17970.46
## ARIMA(1,1,1) with drift : 17969.53
## ARIMA(0,1,1) with drift : 17966.98
## ARIMA(0,1,1)(1,0,0)[260] with drift : Inf
## ARIMA(0,1,1)(1,0,1)[260] with drift : Inf
## ARIMA(0,1,2) with drift : 17968.91
## ARIMA(1,1,2) with drift : Inf
## ARIMA(0,1,1) : 17969.15
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,1,1) with drift : 17973.84
##
## Best model: ARIMA(0,1,1) with drift
forecaste_ftse <- forecast(fit_ftse, 150)
plot(forecaste_ftse, main = "Graph with forecasting of ftse",col.main = "darkgreen")
print(forecaste_ftse)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 1998.650 5464.642 5425.690 5503.594 5405.070 5524.214
## 1998.654 5466.263 5407.555 5524.970 5376.477 5556.048
## 1998.658 5467.883 5394.563 5541.204 5355.749 5580.017
## 1998.662 5469.504 5384.033 5554.974 5338.788 5600.220
## 1998.665 5471.124 5375.028 5567.221 5324.157 5618.091
## 1998.669 5472.745 5367.086 5578.404 5311.153 5634.337
## 1998.673 5474.366 5359.940 5588.791 5299.367 5649.364
## 1998.677 5475.986 5353.420 5598.552 5288.537 5663.435
## 1998.681 5477.607 5347.408 5607.806 5278.484 5676.729
## 1998.685 5479.227 5341.819 5616.636 5269.079 5689.376
## 1998.688 5480.848 5336.590 5625.106 5260.224 5701.472
## 1998.692 5482.468 5331.671 5633.266 5251.844 5713.093
## 1998.696 5484.089 5327.025 5641.153 5243.881 5724.298
## 1998.700 5485.710 5322.620 5648.800 5236.285 5735.135
## 1998.704 5487.330 5318.429 5656.232 5229.018 5745.643
## 1998.708 5488.951 5314.431 5663.470 5222.046 5755.855
## 1998.712 5490.571 5310.609 5670.534 5215.343 5765.800
## 1998.715 5492.192 5306.947 5677.437 5208.884 5775.500
## 1998.719 5493.813 5303.431 5684.194 5202.650 5784.976
## 1998.723 5495.433 5300.051 5690.816 5196.622 5794.245
## 1998.727 5497.054 5296.795 5697.313 5190.784 5803.323
## 1998.731 5498.674 5293.655 5703.694 5185.124 5812.225
## 1998.735 5500.295 5290.623 5709.967 5179.630 5820.960
## 1998.738 5501.916 5287.692 5716.139 5174.290 5829.542
## 1998.742 5503.536 5284.856 5722.216 5169.094 5837.978
## 1998.746 5505.157 5282.109 5728.204 5164.035 5846.279
## 1998.750 5506.777 5279.446 5734.109 5159.104 5854.451
## 1998.754 5508.398 5276.862 5739.934 5154.294 5862.502
## 1998.758 5510.019 5274.353 5745.684 5149.600 5870.438
## 1998.762 5511.639 5271.915 5751.363 5145.013 5878.265
## 1998.765 5513.260 5269.545 5756.975 5140.530 5885.989
## 1998.769 5514.880 5267.239 5762.522 5136.146 5893.615
## 1998.773 5516.501 5264.995 5768.007 5131.855 5901.147
## 1998.777 5518.122 5262.809 5773.435 5127.654 5908.589
## 1998.781 5519.742 5260.678 5778.806 5123.538 5915.946
## 1998.785 5521.363 5258.602 5784.124 5119.504 5923.221
## 1998.788 5522.983 5256.576 5789.391 5115.549 5930.418
## 1998.792 5524.604 5254.600 5794.608 5111.669 5937.539
## 1998.796 5526.225 5252.671 5799.778 5107.861 5944.588
## 1998.800 5527.845 5250.788 5804.902 5104.123 5951.568
## 1998.804 5529.466 5248.948 5809.983 5100.451 5958.480
## 1998.808 5531.086 5247.151 5815.022 5096.845 5965.328
## 1998.812 5532.707 5245.394 5820.020 5093.300 5972.114
## 1998.815 5534.328 5243.677 5824.979 5089.815 5978.840
## 1998.819 5535.948 5241.997 5829.899 5086.389 5985.508
## 1998.823 5537.569 5240.354 5834.784 5083.018 5992.120
## 1998.827 5539.189 5238.747 5839.632 5079.702 5998.677
## 1998.831 5540.810 5237.173 5844.447 5076.438 6005.182
## 1998.835 5542.431 5235.633 5849.228 5073.225 6011.637
## 1998.838 5544.051 5234.126 5853.977 5070.061 6018.042
## 1998.842 5545.672 5232.649 5858.695 5066.945 6024.399
## 1998.846 5547.292 5231.203 5863.382 5063.875 6030.710
## 1998.850 5548.913 5229.786 5868.040 5060.851 6036.975
## 1998.854 5550.534 5228.398 5872.669 5057.870 6043.197
## 1998.858 5552.154 5227.038 5877.270 5054.932 6049.376
## 1998.862 5553.775 5225.705 5881.845 5052.035 6055.514
## 1998.865 5555.395 5224.398 5886.393 5049.179 6061.612
## 1998.869 5557.016 5223.117 5890.915 5046.362 6067.670
## 1998.873 5558.637 5221.861 5895.412 5043.583 6073.690
## 1998.877 5560.257 5220.629 5899.885 5040.841 6079.673
## 1998.881 5561.878 5219.421 5904.334 5038.136 6085.620
## 1998.885 5563.498 5218.237 5908.760 5035.466 6091.531
## 1998.888 5565.119 5217.074 5913.164 5032.831 6097.407
## 1998.892 5566.740 5215.934 5917.545 5030.229 6103.250
## 1998.896 5568.360 5214.816 5921.905 5027.661 6109.060
## 1998.900 5569.981 5213.718 5926.243 5025.124 6114.837
## 1998.904 5571.601 5212.641 5930.561 5022.619 6120.583
## 1998.908 5573.222 5211.585 5934.859 5020.145 6126.299
## 1998.912 5574.843 5210.547 5939.138 5017.701 6131.984
## 1998.915 5576.463 5209.530 5943.397 5015.287 6137.640
## 1998.919 5578.084 5208.531 5947.637 5012.901 6143.267
## 1998.923 5579.704 5207.550 5951.859 5010.543 6148.865
## 1998.927 5581.325 5206.587 5956.063 5008.213 6154.437
## 1998.931 5582.946 5205.643 5960.249 5005.910 6159.981
## 1998.935 5584.566 5204.715 5964.417 5003.634 6165.498
## 1998.938 5586.187 5203.805 5968.569 5001.384 6170.990
## 1998.942 5587.807 5202.911 5972.704 4999.159 6176.456
## 1998.946 5589.428 5202.033 5976.823 4996.959 6181.897
## 1998.950 5591.049 5201.171 5980.926 4994.783 6187.314
## 1998.954 5592.669 5200.326 5985.013 4992.631 6192.707
## 1998.958 5594.290 5199.495 5989.084 4990.504 6198.076
## 1998.962 5595.910 5198.680 5993.141 4988.399 6203.422
## 1998.965 5597.531 5197.879 5997.183 4986.317 6208.745
## 1998.969 5599.152 5197.093 6001.210 4984.257 6214.046
## 1998.973 5600.772 5196.322 6005.222 4982.219 6219.326
## 1998.977 5602.393 5195.564 6009.221 4980.202 6224.583
## 1998.981 5604.013 5194.821 6013.206 4978.207 6229.820
## 1998.985 5605.634 5194.090 6017.177 4976.233 6235.035
## 1998.988 5607.255 5193.374 6021.135 4974.278 6240.231
## 1998.992 5608.875 5192.670 6025.080 4972.344 6245.406
## 1998.996 5610.496 5191.979 6029.012 4970.430 6250.561
## 1999.000 5612.116 5191.301 6032.931 4968.535 6255.697
## 1999.004 5613.737 5190.636 6036.838 4966.660 6260.814
## 1999.008 5615.358 5189.982 6040.733 4964.803 6265.913
## 1999.012 5616.978 5189.341 6044.615 4962.964 6270.992
## 1999.015 5618.599 5188.712 6048.485 4961.144 6276.054
## 1999.019 5620.219 5188.094 6052.344 4959.341 6281.097
## 1999.023 5621.840 5187.488 6056.191 4957.557 6286.123
## 1999.027 5623.461 5186.894 6060.027 4955.789 6291.132
## 1999.031 5625.081 5186.310 6063.852 4954.039 6296.123
## 1999.035 5626.702 5185.738 6067.666 4952.306 6301.098
## 1999.038 5628.322 5185.176 6071.468 4950.589 6306.056
## 1999.042 5629.943 5184.625 6075.261 4948.888 6310.998
## 1999.046 5631.564 5184.085 6079.042 4947.204 6315.923
## 1999.050 5633.184 5183.555 6082.813 4945.536 6320.833
## 1999.054 5634.805 5183.035 6086.574 4943.883 6325.727
## 1999.058 5636.425 5182.525 6090.325 4942.245 6330.605
## 1999.062 5638.046 5182.026 6094.066 4940.623 6335.469
## 1999.065 5639.667 5181.536 6097.797 4939.016 6340.317
## 1999.069 5641.287 5181.056 6101.519 4937.424 6345.150
## 1999.073 5642.908 5180.585 6105.231 4935.846 6349.969
## 1999.077 5644.528 5180.124 6108.933 4934.283 6354.774
## 1999.081 5646.149 5179.672 6112.626 4932.734 6359.564
## 1999.085 5647.770 5179.229 6116.310 4931.198 6364.341
## 1999.088 5649.390 5178.795 6119.985 4929.677 6369.103
## 1999.092 5651.011 5178.370 6123.651 4928.170 6373.852
## 1999.096 5652.631 5177.954 6127.308 4926.675 6378.587
## 1999.100 5654.252 5177.547 6130.957 4925.195 6383.309
## 1999.104 5655.872 5177.148 6134.597 4923.727 6388.018
## 1999.108 5657.493 5176.758 6138.228 4922.272 6392.714
## 1999.112 5659.114 5176.376 6141.851 4920.830 6397.397
## 1999.115 5660.734 5176.003 6145.466 4919.401 6402.068
## 1999.119 5662.355 5175.637 6149.073 4917.984 6406.725
## 1999.123 5663.975 5175.280 6152.671 4916.580 6411.371
## 1999.127 5665.596 5174.930 6156.262 4915.188 6416.005
## 1999.131 5667.217 5174.589 6159.844 4913.807 6420.626
## 1999.135 5668.837 5174.255 6163.419 4912.439 6425.235
## 1999.138 5670.458 5173.929 6166.987 4911.083 6429.833
## 1999.142 5672.078 5173.611 6170.546 4909.738 6434.419
## 1999.146 5673.699 5173.300 6174.098 4908.404 6438.994
## 1999.150 5675.320 5172.996 6177.643 4907.082 6443.557
## 1999.154 5676.940 5172.700 6181.180 4905.772 6448.109
## 1999.158 5678.561 5172.411 6184.710 4904.472 6452.650
## 1999.162 5680.181 5172.130 6188.233 4903.183 6457.180
## 1999.165 5681.802 5171.855 6191.749 4901.905 6461.699
## 1999.169 5683.423 5171.587 6195.258 4900.638 6466.207
## 1999.173 5685.043 5171.327 6198.760 4899.382 6470.705
## 1999.177 5686.664 5171.073 6202.255 4898.136 6475.192
## 1999.181 5688.284 5170.826 6205.743 4896.900 6479.669
## 1999.185 5689.905 5170.586 6209.224 4895.675 6484.136
## 1999.188 5691.526 5170.352 6212.699 4894.459 6488.592
## 1999.192 5693.146 5170.125 6216.168 4893.254 6493.038
## 1999.196 5694.767 5169.904 6219.629 4892.059 6497.475
## 1999.200 5696.387 5169.690 6223.085 4890.874 6501.901
## 1999.204 5698.008 5169.483 6226.534 4889.698 6506.318
## 1999.208 5699.629 5169.281 6229.976 4888.532 6510.725
## 1999.212 5701.249 5169.086 6233.413 4887.376 6515.123
## 1999.215 5702.870 5168.897 6236.843 4886.229 6519.511
## 1999.219 5704.490 5168.714 6240.267 4885.091 6523.890
## 1999.223 5706.111 5168.537 6243.685 4883.963 6528.260
smi=(EuStockMarkets[,2])
plot(smi)
components.ts = decompose(smi)
plot(components.ts)
fit_smi <- auto.arima(smi, trace=TRUE)
##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,2,2)(1,0,1)[260] : Inf
## ARIMA(0,2,0) : 20131.81
## ARIMA(1,2,0)(1,0,0)[260] : Inf
## ARIMA(0,2,1)(0,0,1)[260] : Inf
## ARIMA(0,2,0)(1,0,0)[260] : Inf
## ARIMA(0,2,0)(0,0,1)[260] : Inf
## ARIMA(0,2,0)(1,0,1)[260] : Inf
## ARIMA(1,2,0) : 19656.54
## ARIMA(1,2,0)(0,0,1)[260] : Inf
## ARIMA(1,2,0)(1,0,1)[260] : Inf
## ARIMA(2,2,0) : 19471.95
## ARIMA(2,2,0)(1,0,0)[260] : Inf
## ARIMA(2,2,0)(0,0,1)[260] : Inf
## ARIMA(2,2,0)(1,0,1)[260] : Inf
## ARIMA(3,2,0) : 19389.41
## ARIMA(3,2,0)(1,0,0)[260] : Inf
## ARIMA(3,2,0)(0,0,1)[260] : Inf
## ARIMA(3,2,0)(1,0,1)[260] : Inf
## ARIMA(4,2,0) : 19351.77
## ARIMA(4,2,0)(1,0,0)[260] : Inf
## ARIMA(4,2,0)(0,0,1)[260] : Inf
## ARIMA(4,2,0)(1,0,1)[260] : Inf
## ARIMA(5,2,0) : 19282.73
## ARIMA(5,2,0)(1,0,0)[260] : Inf
## ARIMA(5,2,0)(0,0,1)[260] : Inf
## ARIMA(5,2,0)(1,0,1)[260] : Inf
## ARIMA(5,2,1) : Inf
## ARIMA(4,2,1) : Inf
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(5,2,0) : 19295.02
##
## Best model: ARIMA(5,2,0)
forecaste_smi <- forecast(fit_smi, 150)
plot(forecaste_smi, main = "Graph with forecasting of smi",col.main = "darkgreen")
print(forecaste_smi)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 1998.650 7687.499 7631.83090 7743.168 7602.36172 7772.637
## 1998.654 7652.238 7563.18203 7741.293 7516.03889 7788.436
## 1998.658 7617.448 7495.74729 7739.148 7431.32291 7803.573
## 1998.662 7646.633 7490.80986 7802.457 7408.32188 7884.945
## 1998.665 7644.052 7451.92849 7836.176 7350.22426 7937.880
## 1998.669 7664.777 7434.10988 7895.444 7312.00220 8017.551
## 1998.673 7668.581 7393.15781 7944.004 7247.35772 8089.804
## 1998.677 7666.203 7344.07701 7988.329 7173.55370 8158.853
## 1998.681 7664.865 7294.12510 8035.604 7097.86750 8231.862
## 1998.685 7672.903 7251.52019 8094.287 7028.45340 8317.353
## 1998.688 7676.172 7202.08064 8150.262 6951.11208 8401.231
## 1998.692 7682.438 7153.62980 8211.246 6873.69566 8491.180
## 1998.696 7686.193 7100.28876 8272.097 6790.12987 8582.256
## 1998.700 7689.157 7044.30095 8334.014 6702.93465 8675.380
## 1998.704 7692.413 6986.80416 8398.023 6613.27722 8771.549
## 1998.708 7697.032 6928.89039 8465.173 6522.26091 8871.803
## 1998.712 7700.925 6868.50419 8533.346 6427.84717 8974.003
## 1998.715 7705.198 6806.79484 8603.602 6331.20874 9079.188
## 1998.719 7709.104 6743.00807 8675.200 6231.58780 9186.620
## 1998.723 7712.914 6677.51184 8748.316 6129.40315 9296.424
## 1998.727 7716.786 6610.50075 8823.071 6024.86874 9408.703
## 1998.731 7720.854 6542.13781 8899.570 5918.16313 9523.545
## 1998.735 7724.811 6472.14567 8977.476 5809.02475 9640.597
## 1998.738 7728.815 6400.71350 9056.917 5697.65897 9759.971
## 1998.742 7732.766 6327.76405 9137.769 5584.00075 9881.532
## 1998.746 7736.707 6253.37408 9220.040 5468.14514 10005.269
## 1998.750 7740.659 6177.59172 9303.727 5350.15378 10131.165
## 1998.754 7744.639 6100.45656 9388.822 5230.07875 10259.200
## 1998.758 7748.602 6021.94634 9475.258 5107.90983 10389.295
## 1998.762 7752.571 5942.10613 9563.036 4983.70379 10521.439
## 1998.765 7756.533 5860.94293 9652.122 4857.47840 10655.587
## 1998.769 7760.493 5778.48425 9742.501 4729.27228 10791.713
## 1998.773 7764.455 5694.75230 9834.158 4599.11778 10929.793
## 1998.777 7768.421 5609.76712 9927.076 4467.04453 11069.798
## 1998.781 7772.385 5523.53961 10021.231 4333.07273 11211.697
## 1998.785 7776.349 5436.09000 10116.609 4197.23151 11355.467
## 1998.788 7780.313 5347.43262 10213.193 4059.54372 11501.082
## 1998.792 7784.276 5257.58413 10310.968 3920.03432 11648.517
## 1998.796 7788.239 5166.55990 10409.919 3778.72658 11797.752
## 1998.800 7792.204 5074.37449 10510.033 3635.64270 11948.764
## 1998.804 7796.167 4981.04082 10611.294 3490.80294 12101.531
## 1998.808 7800.131 4886.57281 10713.689 3344.22829 12256.034
## 1998.812 7804.095 4790.98316 10817.206 3195.93831 12412.251
## 1998.815 7808.058 4694.28453 10921.832 3045.95230 12570.164
## 1998.819 7812.022 4596.48907 11027.555 2894.28881 12729.755
## 1998.823 7815.986 4497.60852 11134.363 2740.96576 12891.006
## 1998.827 7819.949 4397.65405 11242.245 2586.00035 13053.898
## 1998.831 7823.913 4296.63676 11351.189 2429.40948 13218.417
## 1998.835 7827.877 4194.56726 11461.186 2271.20940 13384.544
## 1998.838 7831.840 4091.45593 11572.225 2111.41598 13552.265
## 1998.842 7835.804 3987.31282 11684.295 1950.04458 13721.564
## 1998.846 7839.768 3882.14769 11797.388 1787.11013 13892.426
## 1998.850 7843.732 3775.97000 11911.493 1622.62713 14064.836
## 1998.854 7847.695 3668.78901 12026.601 1456.60969 14238.781
## 1998.858 7851.659 3560.61369 12142.704 1289.07155 14414.246
## 1998.862 7855.623 3451.45277 12259.792 1120.02609 14591.219
## 1998.865 7859.586 3341.31480 12377.858 949.48634 14769.686
## 1998.869 7863.550 3230.20805 12496.892 777.46498 14949.635
## 1998.873 7867.514 3118.14062 12616.887 603.97438 15131.053
## 1998.877 7871.477 3005.12041 12737.834 429.02663 15313.928
## 1998.881 7875.441 2891.15511 12859.727 252.63350 15498.249
## 1998.885 7879.405 2776.25225 12982.557 74.80647 15684.003
## 1998.888 7883.368 2660.41915 13106.318 -104.44321 15871.180
## 1998.892 7887.332 2543.66300 13231.001 -285.10459 16059.769
## 1998.896 7891.296 2425.99079 13356.601 -467.16696 16249.759
## 1998.900 7895.260 2307.40939 13483.110 -650.61982 16441.139
## 1998.904 7899.223 2187.92547 13610.521 -835.45295 16633.899
## 1998.908 7903.187 2067.54561 13738.828 -1021.65632 16828.030
## 1998.912 7907.151 1946.27621 13868.025 -1209.22012 17023.521
## 1998.915 7911.114 1824.12354 13998.105 -1398.13476 17220.363
## 1998.919 7915.078 1701.09375 14129.062 -1588.39084 17418.547
## 1998.923 7919.042 1577.19286 14260.891 -1779.97915 17618.063
## 1998.927 7923.005 1452.42676 14393.584 -1972.89069 17818.902
## 1998.931 7926.969 1326.80123 14527.137 -2167.11661 18021.055
## 1998.935 7930.933 1200.32194 14661.544 -2362.64825 18224.514
## 1998.938 7934.897 1072.99443 14796.799 -2559.47712 18429.270
## 1998.942 7938.860 944.82416 14932.896 -2757.59489 18635.315
## 1998.946 7942.824 815.81646 15069.831 -2956.99339 18842.641
## 1998.950 7946.788 685.97658 15207.599 -3157.66460 19051.240
## 1998.954 7950.751 555.30967 15346.193 -3359.60066 19261.103
## 1998.958 7954.715 423.82076 15485.609 -3562.79384 19472.224
## 1998.962 7958.679 291.51483 15625.843 -3767.23656 19684.594
## 1998.965 7962.642 158.39674 15766.888 -3972.92136 19898.206
## 1998.969 7966.606 24.47127 15908.741 -4179.84094 20113.053
## 1998.973 7970.570 -110.25687 16051.396 -4387.98811 20329.128
## 1998.977 7974.533 -245.78306 16194.850 -4597.35579 20546.423
## 1998.981 7978.497 -382.10277 16339.097 -4807.93705 20764.931
## 1998.985 7982.461 -519.21153 16484.133 -5019.72505 20984.647
## 1998.988 7986.425 -657.10495 16629.954 -5232.71309 21205.562
## 1998.992 7990.388 -795.77871 16776.555 -5446.89456 21427.671
## 1998.996 7994.352 -935.22857 16923.933 -5662.26297 21650.967
## 1999.000 7998.316 -1075.45035 17072.082 -5878.81193 21875.443
## 1999.004 8002.279 -1216.43994 17220.999 -6096.53516 22101.094
## 1999.008 8006.243 -1358.19329 17370.679 -6315.42645 22327.913
## 1999.012 8010.207 -1500.70642 17521.120 -6535.47973 22555.893
## 1999.015 8014.170 -1643.97541 17672.316 -6756.68900 22785.030
## 1999.019 8018.134 -1787.99640 17824.265 -6979.04834 23015.317
## 1999.023 8022.098 -1932.76558 17976.961 -7202.55195 23246.748
## 1999.027 8026.062 -2078.27921 18130.402 -7427.19410 23479.317
## 1999.031 8030.025 -2224.53361 18284.584 -7652.96915 23713.020
## 1999.035 8033.989 -2371.52513 18439.503 -7879.87153 23947.849
## 1999.038 8037.953 -2519.25019 18595.155 -8107.89577 24183.801
## 1999.042 8041.916 -2667.70526 18751.538 -8337.03646 24420.869
## 1999.046 8045.880 -2816.88686 18908.647 -8567.28829 24659.048
## 1999.050 8049.844 -2966.79157 19066.479 -8798.64601 24898.333
## 1999.054 8053.807 -3117.41600 19225.031 -9031.10445 25138.719
## 1999.058 8057.771 -3268.75681 19384.299 -9264.65850 25380.201
## 1999.062 8061.735 -3420.81071 19544.280 -9499.30313 25622.773
## 1999.065 8065.698 -3573.57446 19704.971 -9735.03338 25866.430
## 1999.069 8069.662 -3727.04487 19866.369 -9971.84436 26111.169
## 1999.073 8073.626 -3881.21876 20028.471 -10209.73123 26356.983
## 1999.077 8077.590 -4036.09302 20191.272 -10448.68924 26603.868
## 1999.081 8081.553 -4191.66459 20354.771 -10688.71367 26851.820
## 1999.085 8085.517 -4347.93042 20518.964 -10929.79989 27100.834
## 1999.088 8089.481 -4504.88753 20683.849 -11171.94332 27350.905
## 1999.092 8093.444 -4662.53294 20849.422 -11415.13943 27602.028
## 1999.096 8097.408 -4820.86375 21015.680 -11659.38376 27854.200
## 1999.100 8101.372 -4979.87707 21182.621 -11904.67190 28107.415
## 1999.104 8105.335 -5139.57005 21350.241 -12150.99950 28361.670
## 1999.108 8109.299 -5299.93989 21518.538 -12398.36225 28616.961
## 1999.112 8113.263 -5460.98381 21687.509 -12646.75592 28873.282
## 1999.115 8117.227 -5622.69906 21857.152 -12896.17631 29130.629
## 1999.119 8121.190 -5785.08293 22027.463 -13146.61927 29389.000
## 1999.123 8125.154 -5948.13275 22198.441 -13398.08070 29648.389
## 1999.127 8129.118 -6111.84588 22370.081 -13650.55658 29908.792
## 1999.131 8133.081 -6276.21969 22542.382 -13904.04289 30170.206
## 1999.135 8137.045 -6441.25161 22715.342 -14158.53568 30432.626
## 1999.138 8141.009 -6606.93909 22888.957 -14414.03106 30696.048
## 1999.142 8144.972 -6773.27959 23063.224 -14670.52517 30960.470
## 1999.146 8148.936 -6940.27063 23238.143 -14928.01418 31225.886
## 1999.150 8152.900 -7107.90974 23413.709 -15186.49433 31492.294
## 1999.154 8156.863 -7276.19448 23589.921 -15445.96188 31759.689
## 1999.158 8160.827 -7445.12244 23766.777 -15706.41315 32028.068
## 1999.162 8164.791 -7614.69124 23944.273 -15967.84450 32297.426
## 1999.165 8168.755 -7784.89851 24122.408 -16230.25232 32567.761
## 1999.169 8172.718 -7955.74193 24301.178 -16493.63303 32839.070
## 1999.173 8176.682 -8127.21919 24480.583 -16757.98312 33111.347
## 1999.177 8180.646 -8299.32800 24660.619 -17023.29909 33384.590
## 1999.181 8184.609 -8472.06612 24841.285 -17289.57749 33658.796
## 1999.185 8188.573 -8645.43130 25022.577 -17556.81491 33933.961
## 1999.188 8192.537 -8819.42134 25204.495 -17825.00796 34210.081
## 1999.192 8196.500 -8994.03404 25387.035 -18094.15331 34487.154
## 1999.196 8200.464 -9169.26726 25570.196 -18364.24764 34765.176
## 1999.200 8204.428 -9345.11884 25753.975 -18635.28768 35044.143
## 1999.204 8208.392 -9521.58667 25938.370 -18907.27018 35324.053
## 1999.208 8212.355 -9698.66864 26123.379 -19180.19194 35604.902
## 1999.212 8216.319 -9876.36269 26309.001 -19454.04979 35886.688
## 1999.215 8220.283 -10054.66675 26495.232 -19728.84058 36169.406
## 1999.219 8224.246 -10233.57880 26682.071 -20004.56119 36453.054
## 1999.223 8228.210 -10413.09681 26869.517 -20281.20855 36737.629
dax=(EuStockMarkets[,1])
plot(dax)
components.ts = decompose(dax)
plot(components.ts)
fit_dax <- auto.arima(dax, trace=TRUE)
##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,2,2)(1,0,1)[260] : Inf
## ARIMA(0,2,0) : 19475.21
## ARIMA(1,2,0)(1,0,0)[260] : Inf
## ARIMA(0,2,1)(0,0,1)[260] : Inf
## ARIMA(0,2,0)(1,0,0)[260] : Inf
## ARIMA(0,2,0)(0,0,1)[260] : Inf
## ARIMA(0,2,0)(1,0,1)[260] : Inf
## ARIMA(1,2,0) : 18963.57
## ARIMA(1,2,0)(0,0,1)[260] : Inf
## ARIMA(1,2,0)(1,0,1)[260] : Inf
## ARIMA(2,2,0) : 18749.75
## ARIMA(2,2,0)(1,0,0)[260] : Inf
## ARIMA(2,2,0)(0,0,1)[260] : Inf
## ARIMA(2,2,0)(1,0,1)[260] : Inf
## ARIMA(3,2,0) : 18635.06
## ARIMA(3,2,0)(1,0,0)[260] : Inf
## ARIMA(3,2,0)(0,0,1)[260] : Inf
## ARIMA(3,2,0)(1,0,1)[260] : Inf
## ARIMA(4,2,0) : 18584.6
## ARIMA(4,2,0)(1,0,0)[260] : Inf
## ARIMA(4,2,0)(0,0,1)[260] : Inf
## ARIMA(4,2,0)(1,0,1)[260] : Inf
## ARIMA(5,2,0) : 18495.78
## ARIMA(5,2,0)(1,0,0)[260] : Inf
## ARIMA(5,2,0)(0,0,1)[260] : Inf
## ARIMA(5,2,0)(1,0,1)[260] : Inf
## ARIMA(5,2,1) : 18223.75
## ARIMA(5,2,1)(1,0,0)[260] : Inf
## ARIMA(5,2,1)(0,0,1)[260] : Inf
## ARIMA(5,2,1)(1,0,1)[260] : Inf
## ARIMA(4,2,1) : Inf
## ARIMA(5,2,2) : Inf
## ARIMA(4,2,2) : Inf
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(5,2,1) : Inf
## ARIMA(5,2,0) : 18508.04
##
## Best model: ARIMA(5,2,0)
forecaste_dax <- forecast(fit_dax, 150)
plot(forecaste_dax, main = "Graph with forecasting of dax",col.main = "darkgreen")
print(forecaste_dax)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 1998.650 5477.071 5432.02996 5522.113 5408.18642 5545.957
## 1998.654 5455.437 5385.72621 5525.148 5348.82337 5562.051
## 1998.658 5438.930 5345.83957 5532.020 5296.56051 5581.299
## 1998.662 5470.902 5353.45411 5588.349 5291.28107 5650.522
## 1998.665 5478.529 5334.55983 5622.498 5258.34723 5698.710
## 1998.669 5505.691 5333.18248 5678.199 5241.86212 5769.519
## 1998.673 5512.314 5306.11510 5718.513 5196.95988 5827.669
## 1998.677 5517.260 5276.48198 5758.037 5149.02196 5885.497
## 1998.681 5524.894 5248.36282 5801.426 5101.97581 5947.813
## 1998.685 5540.523 5226.76715 5854.279 5060.67485 6020.371
## 1998.688 5551.386 5198.74638 5904.026 5012.07011 6090.702
## 1998.692 5564.652 5171.57225 5957.732 4963.48846 6165.815
## 1998.696 5574.519 5139.17198 6009.867 4908.71301 6240.326
## 1998.700 5584.631 5105.76102 6063.500 4852.26279 6316.998
## 1998.704 5595.439 5071.76273 6119.116 4794.54513 6396.333
## 1998.708 5607.468 5037.67149 6177.265 4736.03925 6478.897
## 1998.712 5618.547 5001.31322 6235.781 4674.56945 6562.524
## 1998.715 5629.916 4963.98087 6295.852 4611.45597 6648.377
## 1998.719 5640.767 4924.86387 6356.669 4545.88789 6735.645
## 1998.723 5651.753 4884.71802 6418.789 4478.67404 6824.833
## 1998.727 5662.881 4843.55822 6482.203 4409.83510 6915.926
## 1998.731 5674.177 4801.42576 6546.928 4339.41932 7008.934
## 1998.735 5685.286 4757.98422 6612.588 4267.10015 7103.472
## 1998.738 5696.434 4713.48573 6679.383 4193.14411 7199.725
## 1998.742 5707.511 4667.83780 6747.183 4117.46828 7297.553
## 1998.746 5718.625 4621.18019 6816.069 4040.22809 7397.022
## 1998.750 5729.763 4573.51383 6886.012 3961.43262 7498.093
## 1998.754 5740.921 4524.85105 6956.990 3881.10266 7600.739
## 1998.758 5752.044 4475.15311 7028.934 3799.20816 7704.879
## 1998.762 5763.173 4424.47891 7101.867 3715.81718 7810.528
## 1998.765 5774.293 4372.82833 7175.758 3630.93759 7917.649
## 1998.769 5785.422 4320.23458 7250.610 3544.61107 8026.233
## 1998.773 5796.554 4266.70582 7326.403 3456.85286 8136.256
## 1998.777 5807.688 4212.25375 7403.123 3367.68162 8247.695
## 1998.781 5818.816 4156.88315 7480.749 3277.10896 8360.523
## 1998.785 5829.945 4100.61431 7559.276 3185.16182 8474.729
## 1998.788 5841.073 4043.45681 7638.690 3091.85605 8590.291
## 1998.792 5852.203 3985.42473 7718.982 2997.21186 8707.195
## 1998.796 5863.333 3926.52760 7800.139 2901.24452 8825.422
## 1998.800 5874.464 3866.77568 7882.152 2803.96987 8944.957
## 1998.804 5885.593 3806.17809 7965.007 2705.40246 9065.783
## 1998.808 5896.722 3744.74611 8048.698 2605.55878 9187.886
## 1998.812 5907.852 3682.48886 8133.214 2504.45299 9311.250
## 1998.815 5918.981 3619.41589 8218.547 2402.09950 9435.863
## 1998.819 5930.111 3555.53576 8304.686 2298.51159 9561.710
## 1998.823 5941.241 3490.85706 8391.624 2193.70237 9688.779
## 1998.827 5952.370 3425.38798 8479.352 2087.68447 9817.056
## 1998.831 5963.500 3359.13686 8567.862 1980.47049 9946.529
## 1998.835 5974.629 3292.11145 8657.147 1872.07234 10077.186
## 1998.838 5985.759 3224.31940 8747.198 1762.50169 10209.016
## 1998.842 5996.888 3155.76803 8838.009 1651.76977 10342.007
## 1998.846 6008.018 3086.46452 8929.571 1539.88756 10476.148
## 1998.850 6019.147 3016.41583 9021.879 1426.86570 10611.429
## 1998.854 6030.277 2945.62878 9114.925 1312.71461 10747.840
## 1998.858 6041.407 2874.10996 9208.703 1197.44438 10885.369
## 1998.862 6052.536 2801.86580 9303.207 1081.06484 11024.008
## 1998.865 6063.666 2728.90256 9398.429 963.58554 11163.746
## 1998.869 6074.795 2655.22633 9494.364 845.01583 11304.575
## 1998.873 6085.925 2580.84306 9591.007 725.36480 11446.485
## 1998.877 6097.054 2505.75855 9688.350 604.64132 11589.468
## 1998.881 6108.184 2429.97848 9786.390 482.85405 11733.514
## 1998.885 6119.314 2353.50835 9885.119 360.01145 11878.616
## 1998.888 6130.443 2276.35357 9984.533 236.12176 12024.765
## 1998.892 6141.573 2198.51941 10084.626 111.19305 12171.953
## 1998.896 6152.702 2120.01102 10185.394 -14.76681 12320.172
## 1998.900 6163.832 2040.83344 10286.830 -141.75012 12469.414
## 1998.904 6174.961 1960.99158 10388.931 -269.74933 12619.672
## 1998.908 6186.091 1880.49028 10491.692 -398.75710 12770.939
## 1998.912 6197.221 1799.33423 10595.107 -528.76620 12923.207
## 1998.915 6208.350 1717.52806 10699.172 -659.76958 13076.470
## 1998.919 6219.480 1635.07628 10803.883 -791.76033 13230.720
## 1998.923 6230.609 1551.98332 10909.235 -924.73168 13385.950
## 1998.927 6241.739 1468.25352 11015.224 -1058.67701 13542.155
## 1998.931 6252.868 1383.89111 11121.846 -1193.58981 13699.327
## 1998.935 6263.998 1298.90027 11229.096 -1329.46372 13857.460
## 1998.938 6275.128 1213.28509 11336.970 -1466.29250 14016.548
## 1998.942 6286.257 1127.04955 11445.465 -1604.07001 14176.584
## 1998.946 6297.387 1040.19760 11554.576 -1742.79025 14337.564
## 1998.950 6308.516 952.73308 11664.300 -1882.44732 14499.480
## 1998.954 6319.646 864.65978 11774.632 -2023.03544 14662.327
## 1998.958 6330.775 775.98142 11885.570 -2164.54893 14826.100
## 1998.962 6341.905 686.70164 11997.108 -2306.98221 14990.792
## 1998.965 6353.035 596.82402 12109.245 -2450.32981 15156.399
## 1998.969 6364.164 506.35208 12221.976 -2594.58634 15322.915
## 1998.973 6375.294 415.28928 12335.298 -2739.74651 15490.334
## 1998.977 6386.423 323.63902 12449.208 -2885.80514 15658.652
## 1998.981 6397.553 231.40463 12563.701 -3032.75710 15827.863
## 1998.985 6408.682 138.58939 12678.776 -3180.59739 15997.962
## 1998.988 6419.812 45.19655 12794.428 -3329.32106 16168.945
## 1998.992 6430.942 -48.77074 12910.654 -3478.92326 16340.807
## 1998.996 6442.071 -143.30934 13027.452 -3629.39922 16513.542
## 1999.000 6453.201 -238.41619 13144.818 -3780.74422 16687.146
## 1999.004 6464.330 -334.08825 13262.749 -3932.95366 16861.614
## 1999.008 6475.460 -430.32256 13381.242 -4086.02297 17036.943
## 1999.012 6486.589 -527.11618 13500.295 -4239.94768 17213.127
## 1999.015 6497.719 -624.46623 13619.904 -4394.72337 17390.161
## 1999.019 6508.849 -722.36987 13740.067 -4550.34571 17568.043
## 1999.023 6519.978 -820.82431 13860.781 -4706.81041 17746.767
## 1999.027 6531.108 -919.82678 13982.042 -4864.11327 17926.329
## 1999.031 6542.237 -1019.37458 14103.849 -5022.25012 18106.725
## 1999.035 6553.367 -1119.46502 14226.199 -5181.21689 18287.951
## 1999.038 6564.496 -1220.09548 14349.088 -5341.00954 18470.002
## 1999.042 6575.626 -1321.26336 14472.515 -5501.62410 18652.876
## 1999.046 6586.756 -1422.96610 14596.477 -5663.05665 18836.568
## 1999.050 6597.885 -1525.20117 14720.972 -5825.30334 19021.074
## 1999.054 6609.015 -1627.96609 14845.996 -5988.36036 19206.390
## 1999.058 6620.144 -1731.25840 14971.547 -6152.22395 19392.513
## 1999.062 6631.274 -1835.07568 15097.623 -6316.89042 19579.438
## 1999.065 6642.403 -1939.41555 15224.222 -6482.35612 19767.163
## 1999.069 6653.533 -2044.27565 15351.342 -6648.61744 19955.684
## 1999.073 6664.663 -2149.65365 15478.979 -6815.67083 20144.996
## 1999.077 6675.792 -2255.54727 15607.132 -6983.51279 20335.097
## 1999.081 6686.922 -2361.95425 15735.798 -7152.13985 20525.983
## 1999.085 6698.051 -2468.87234 15864.975 -7321.54860 20717.651
## 1999.088 6709.181 -2576.29936 15994.661 -7491.73568 20910.097
## 1999.092 6720.310 -2684.23311 16124.854 -7662.69775 21103.319
## 1999.096 6731.440 -2792.67146 16255.552 -7834.43153 21297.312
## 1999.100 6742.570 -2901.61228 16386.751 -8006.93378 21492.073
## 1999.104 6753.699 -3011.05348 16518.452 -8180.20129 21687.600
## 1999.108 6764.829 -3120.99299 16650.650 -8354.23091 21883.888
## 1999.112 6775.958 -3231.42877 16783.345 -8529.01949 22080.936
## 1999.115 6787.088 -3342.35880 16916.535 -8704.56397 22278.740
## 1999.119 6798.217 -3453.78109 17050.216 -8880.86130 22477.296
## 1999.123 6809.347 -3565.69366 17184.388 -9057.90845 22676.603
## 1999.127 6820.477 -3678.09458 17319.048 -9235.70245 22876.656
## 1999.131 6831.606 -3790.98191 17454.194 -9414.24037 23077.453
## 1999.135 6842.736 -3904.35377 17589.825 -9593.51930 23278.991
## 1999.138 6853.865 -4018.20826 17725.939 -9773.53636 23481.267
## 1999.142 6864.995 -4132.54353 17862.533 -9954.28871 23684.278
## 1999.146 6876.124 -4247.35776 17999.607 -10135.77355 23888.022
## 1999.150 6887.254 -4362.64911 18137.157 -10317.98810 24092.496
## 1999.154 6898.384 -4478.41580 18275.183 -10500.92962 24297.697
## 1999.158 6909.513 -4594.65606 18413.682 -10684.59539 24503.622
## 1999.162 6920.643 -4711.36813 18552.654 -10868.98274 24710.268
## 1999.165 6931.772 -4828.55028 18692.095 -11054.08900 24917.634
## 1999.169 6942.902 -4946.20078 18832.005 -11239.91156 25125.715
## 1999.173 6954.031 -5064.31795 18972.381 -11426.44782 25334.511
## 1999.177 6965.161 -5182.90010 19113.222 -11613.69520 25544.017
## 1999.181 6976.291 -5301.94557 19254.527 -11801.65118 25754.232
## 1999.185 6987.420 -5421.45272 19396.293 -11990.31324 25965.154
## 1999.188 6998.550 -5541.41993 19538.519 -12179.67888 26176.778
## 1999.192 7009.679 -5661.84558 19681.204 -12369.74566 26389.104
## 1999.196 7020.809 -5782.72808 19824.346 -12560.51113 26602.129
## 1999.200 7031.938 -5904.06586 19967.943 -12751.97289 26815.850
## 1999.204 7043.068 -6025.85735 20111.993 -12944.12854 27030.265
## 1999.208 7054.198 -6148.10102 20256.496 -13136.97574 27245.371
## 1999.212 7065.327 -6270.79533 20401.450 -13330.51214 27461.166
## 1999.215 7076.457 -6393.93878 20546.852 -13524.73543 27677.649
## 1999.219 7087.586 -6517.52987 20692.702 -13719.64332 27894.816
## 1999.223 7098.716 -6641.56710 20838.999 -13915.23354 28112.665
#library(prophet)
#stocks <- as.data.frame(EuStockMarkets[,4])
#summary(stocks)
#pro_time <- time(EuStockMarkets[,4])
#pro_ftse <- EuStockMarkets[,4]
#head(pro_time)
#df <- data.frame (
# ds = as.POSIXct(pro_time, format="%Y-%m-%d", tz="UTC"),
# y = pro_ftse
#)
#summary(df)
#modpro <- prophet(df)
#forecaste_pro_ftse <- make_future_dataframe(modpro, 100)
#plot(forecaste_pro_ftse, main = "Graph with forecasting of ftse",col.main = "darkgreen")